Consider a homogeneous spherical piece of radioactive material of radius r0 = 5 cm that is generating heat at a constant rate of q.= 3.8x107 W/m3 The heat generated is dissipated to the environment T∞=27°C and h = 110 W/m2°C steadily. The outer surface of the sphere is maintained at a uniform temperature (Ts) and the thermal conductivity of the sphere is k = 25 W/m°C. Assuming steady one-dimensional heat transfer, (a) express the differential equation and the boundary conditions for heat conduction through the sphere, (b) obtain a relation for the variation of temperature in the sphere by solving the differential equation, and (c) determine the temperature at the center of the sphere

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A: The given information in the problem is shown in the following attached image:

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Conduction and Convection

When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a burner, heats up because of the flame underneath it.